HYDRAULIC STRUCTURE CHAPTER3,4.pdf

Chapter 3 GRAVITY DAMS

Basically, gravity dams are solid concrete structures that maintain their stability against design loads from the geometric shape and the weight and strength of the structure. Generally, they are constructed on a straight axis, but may be slightly curved or angled to accommodate the specific site conditions. Gravity dams typically consist of a non-overflow section(s) and an overflow section or spillway. They are constructed with masonry or concrete but of late conventional concrete or roller-compacted concrete are popular. The two general concrete construction methods for concrete gravity dams are conventional placed mass concrete and roller-compacted concrete (RCC). a. Conventional concrete dams.

(1) Conventionally placed mass concrete dams are characterized by construction using materials and techniques employed in the proportioning, mixing, placing, curing, and temperature control of of mass concrete. Construction incorporates methods that have been developed and perfected over many years of designing and building mass concrete dams. The cement hydration process of conventional concrete limits the size and rate of concrete placement and necessitates building in monoliths to meet crack control requirements. Generally using large-size coarse aggregates, mix proportions are selected to produce a low-slump concrete that gives economy, maintains good workability during placement, develops minimum temperature rise during hydration, and produces important properties such as strength, impermeability, and durability. Dam construction with conventional concrete readily facilitates installation of conduits, penstocks, galleries, etc., within the structure. (2) Construction procedures include batching and mixing, and transportation, placement, vibration, cooling, curing, and preparation of horizontal construction joints between between lifts. lifts. The large large volume volume of concrete concrete in a gravity dam normally normally justifies an an onsite batch batch plant, plant, and requires requires an an aggregate aggregate source of adequate adequate quality and quantity, located at or within an economical distance of the project. Transportation from the batch plant to the dam is generally performed in buckets ranging in size from 4 to 12 cubic yards carried by truck, rail, cranes, cableways, or a combination of these methods. The maximum bucket size is usually restricted by the capability of effectively spreading and vibrating the concrete pile after it is dumped from the bucket. The concrete is placed in lifts of 5- to 10-foot depths. Each lift consists of successive layers not exceeding 18 to 20 inches. Vibration is generally performed by large one-man, air-driven, spud-type vibrators. Methods of cleaning horizontal construction joints to remove the weak laitance film on the surface during curing include green cutting, wet sandblasting, and high-pressure air-water jet.

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3) The heat generated as cement hydrates requires careful temperature control during placement of mass concrete and for several days after placement. Uncontrolled heat generation could result in excessive tensile stresses due to extreme gradients within the mass concrete or due to temperature reductions as the concrete approaches its annual temperature cycle. Control measures involve precooling and postcooling techniques to limit the peak temperatures and control the temperature drop. Reduction in the cement content and cement replacement with pozzolans have reduced the temperature-rise potential. Crack control is achieved by constructing the conventional concrete gravity dam in a series of individually stable monoliths separated by transverse contraction joints. Usually, monoliths are approximately 50 feet wide. b. Roller-compacted concrete (RCC) gravity dams.

The design of RCC gravity dams is similar to conventional concrete structures. The differences lie in the construction methods, concrete mix design, and details of the appurtenant structures. Construction of an RCC dam is a relatively new and economical concept. Economic advantages are achieved with rapid placement using construction techniques that are similar to those employed for embankment dams. RCC is a relatively dry, lean, zero slump concrete material containing coarse and fine aggregate that is consolidated by external vibration using vibratory rollers, dozer, and other heavy equipment. In the hardened condition, RCC has similar properties to conventional concrete. For effective consolidation, RCC must be dry enough to support the weight of the construction equipment, but have a consistency wet enough to permit adequate distribution of the past binder throughout the mass during the mixing and vibration process and, thus, achieve the necessary compaction of the RCC and prevention of undesirable segregation and voids. Site Selection a. General. During the feasibility studies, the preliminary site selection will be dependent on the project purposes. purposes. Purposes applicable to dam construction include navigation, flood damage reduction, hydroelectric power generation, fish and wildlife enhancement, water quality, water supply, and recreation. The feasibility study will establish the most suitable and economical location and type of structure. b. Selection factors.

(1) A concrete dam requires a sound bedrock foundation. It is important that the bedrock have adequate shear strength and bearing capacity to meet the















(2) The topography is an important factor in the selection and location of a concrete dam and its appurtenant structures. Construction at a site with a narrow canyon profile on sound bedrock close to the surface is preferable, as this location would minimize the concrete material requirements and the associated costs. (3) The criteria set forth for the spillway, powerhouse, and the other project appurtenances will play an important role in site selection. The relationship and adaptability of these features to the project alignment will need evaluation along with associated costs. (4) Additional factors of lesser importance that need to be included for consideration are the relocation of existing facilities and utilities that lie within the reservoir and in the path of the dam. Included in these are railroads, powerlines, highways, towns, etc. Extensive and costly relocations should be avoided. (5) The method or scheme of diverting flows around or through the damsite during construction is an important consideration to the economy of the dam. A concrete gravity dam offers major advantages and potential cost savings by providing the option of diversion through alternate construction blocks, and lowers risk and delay if overtopping should occur. Forces on Gravity Dams 3-3. Loads a. General . In the design of concrete gravity dams, it is essential to determine the loads required in the stability and stress analysis. The following forces may affect the design:

(1) Dead load. (2) Water Pressure (Headwater and tailwater pressures). (3) Uplift. (4) Temperature. (5) Earth and silt pressures. (6) Ice pressure. (7) Earthquake forces. (8) Wind pressure. (9) Subatmospheric pressure. (10) Wave pressure. (11) Reaction of foundation. b. Dead load .

Dead load comprises the major resisting force. The dead loads considered should include the weight of concrete, superimposed backfill, and appurtenances such as gates and bridges. In the computation of the dead load, relatively small voids such as galleries are normally not deducted except in low dams, where such voids could create an appreciable effect upon the stability of the structure. The cross section of the















acting at its centre of gravity. Unit weight of concrete and masonry is taken as 2400kg/m 3 and 2300kg/m 3. c. Water Pressure; (Headwater and tailwater) . Water pressure is the major external force acting on the dam. As the water is stored in the reservoir, and stands against the body of the dam, it exerts horizontal pressure on the dam.

Max. flow level

h P=1/2 h

Dam

h/3

Fig. G.D. 1 Headwater pressure with vertical vertical upstream face

Head water

h

Tail water P1

P2

Ww

Ww

Fig. G.D. 2 Water pressure for slanted upstream face and water at tailrace

When the upstream face of the dam is vertical, the water pressure P = ½ γh2 and acting at h/3 from base.















Vertical pressure W w = weight of water on slanted side and acting at centre of gravity of volume of water. Uplift Pressure. It is the second major external force acting upwards on the dam. Uplift pressure resulting from headwater and tailwater exists through cross sections within the dam, at the interface between the dam and the foundation, and within the foundation below the base. This pressure is present within the cracks, pores, joints, and seams in the concrete and foundation material. Uplift pressure is an active force that must be included in the stability and stress analysis to ensure structural adequacy. These pressures vary with time and are related to boundary conditions and the permeability of the material. (1) Along the base. (a) General. The uplift pressure will be considered as acting over 100 percent of the base. A hydraulic gradient between the upper and lower pool is developed between the heel and toe of the dam. The pressure distribution along the base and in the foundation is dependent on the effectiveness of drains and grout curtain, where applicable, and geologic features such as rock permeability, seams, jointing, and faulting. The uplift pressure at any point under the structure will be tailwater pressure plus the pressure measured as an ordinate from tailwater to the hydraulic gradient between upper and lower pool.

Fig. G.D.3 Uplift distribution without foundation drainage















(c) With drains. Uplift pressures at the base or below the foundation can be reduced by installing foundation drains. The effectiveness of the drainage system will depend on depth, size, and spacing of the drains; the character of the foundation; and the facility with which the drains can be maintained. This effectiveness will be assumed to vary from 25 to 50 percent, and the design memoranda should contain supporting data for the assumption used. Along the the base, the the uplift pressure will vary vary linearly from the undrained undrained pressure head at the heel, to the reduced pressure head at the line of drains, to the undrained pressure head at the toe, as shown in Figure G.D.4

Figure G.D. 4

Uplift distribution with drainage gallery

Where the line of drains intersects the foundation within a distance of 5 percent of the reservoir depth from the upstream face, the uplift may be assumed to vary as a single straight line, which would be the case if the drains were exactly at the heel. This condition is illustrated in Figure G.D.5 If the drainage gallery is above tailwater elevation, the pressure of the line of drains should be determined as though the tailwater level is equal to the gallery elevation.

















Figure G.D.5. Uplift distribution with foundation drains near upstream face

(d) Grout curtain. For drainage to be controlled economically, retarding of flow to the drains from the upstream head is mandatory. This may be accomplished by a zone of grouting (curtain) or by the natural imperviousness of the foundation. A grouted zone (curtain) should be used wherever the foundation is amenable to grouting. Grout holes shall be oriented to intercept the maximum number of rock fractures to maximize its effectiveness. Under average conditions, the depth of the grout zone should be two-thirds to three-fourths of the headwater-tailwater differential and should be supplemented by foundation drain holes with a depth of at least two-thirds that of the grout zone (curtain).

















Where the foundation is sufficiently impervious to retard the flow and where grouting would be impractical, an artificial cutoff is usually unnecessary. Drains, however, should be provided to relieve the uplift pressures that would build up over a period of time in a relatively impervious medium. In a relatively impervious foundation, drain spacing will be closer than in a relatively permeable foundation. (e) Zero compression zones. Uplift on any portion of any foundation plane not in compression shall be 100 percent of the hydrostatic head of the adjacent face, except where tension is the result of instantaneous loading resulting from earthquake forces. When the zero compression zone does not extend beyond the location of the drains, the uplift will be as shown in Figure G.D.6. For the condition where the zero compression zone extends beyond the drains, drain effectiveness shall not be considered. This uplift condition is shown in Figure G.D.7

















impermeability of intact concrete which precludes the buildup of internal pore pressures. Cracking at the upstream face of an existing dam or weak horizontal construction joints in the body of the dam may affect this assumption. (b) RCC concrete. The determination of the percent uplift will depend on the mix permeability, lift joint treatment, the placements, techniques specified for minimizing segregation within the mixture, compaction methods, and the treatment for watertightness at the upstream and downstream faces. A porous upstream face and lift joints in conjunction with an impermeable downstream face may result in a pressure gradient through a cross section of the dam considerably greater than that outlined above for conventional concrete. Wave Pressure The portions of the dam is subjected to the impact of waves, which is produced in water surface during wind

Water surface

Pw

h

5/3h

2 .4 h

Figure G.D. 8

The wave pressure is tdetermined by the following formula developed by D. A. Molitor

















Wind Load Wind load in stability analysis is usually ignored Earth and Silt

Earth pressures against the dam may occur where backfill is deposited in the foundation excavation and where embankment fills abut and wrap around concrete monoliths. The fill material may or may not be submerged. Silt pressures are considered in the design if suspended sediment measurements indicate that such pressures are expected. Whether the lateral earth pressures will be in an active or an at-rest state is determined by the resulting structure lateral deformation.

Earthquake Forces (1) General. (a) The earthquake loadings used in the design of concrete gravity dams are based on design earthquakes and site-specific motions determined from seismological evaluation. As a minimum, a seismological evaluation should be performed on all projects located in seismic zones. (b) The seismic coefficient method of analysis should be used in determining the resultant location and sliding stability of dams. In strong seismicity areas, a dynamic seismic analysis is required for the internal stress analysis. (c) Earthquake loadings should be checked for horizontal earthquake acceleration and, if included in the stress analysis, vertical acceleration. While an earthquake acceleration might take place in any direction, the analysis should be performed for the most unfavorable direction. (2) Seismic coefficient. The seismic coefficient method of analysis is commonly known as the pseudostatic analysis. Earthquake loading is treated as an inertial

















Figure G.D. 9. Seismically loaded gravity dam, nonoverflow monolith

(a) Inertia of concrete for horizontal earthquake acceleration. The force required to accelerate the concrete mass of the dam is determined from the equation: P e = Ma x =( W/g)αg = W α

Where

Pex = horizontal earthquake force M = mass of dam ax = horizontal earthquake acceleration = g W = weight of dam g = acceleration of gravity a = seismic coefficient coefficient



















Westergaard's approximate equation for Ce, which is sufficiently accurate for all usual conditions, in pound-second feet units is: Ce 

51

 h   1  0.72 1 , 000 t e  

2

where t is the period of vibration. COMBINATION OF FORCES FOR DESIGN The design of a gravity dam is performed through an interative process involving a preliminary layout of the structure followed by a stability and stress analysis. If the structure fails to meet criteria then the layout is modified and reanalyzed. This process is repeated until an acceptable cross section is attained. Analysis Analysis of the stability stability and calculation calculation of of the stresses stresses are generally generally conducted conducted at the dam base and at selected planes within the structure. If weak seams or planes exist in the foundation, they should also be analyzed. Basic Loading Conditions



















(1) Load Condition No. 1 - unusual loading condition - construction. (a) Dam structure completed. (b) No headwater or tailwater. (2) Load Condition No. 2 - usual loading condition - normal operating. (a) Pool elevation at top of closed spillway gates where spillway is gated, and at spillway crest where spillway is ungated. (b) Minimum tailwater. (c) Uplift. (d) Ice and silt pressure, if applicable. (3) Load Condition No. 3 - unusual loading condition - flood discharge. (a) Pool at standard project flood (SPF). (b) Gates at appropriate flood-control openings and tailwater at flood elevation. (c) Tailwater pressure. (d) Uplift. (e) Silt, if applicable. (f) No ice pressure. (4) Load Condition No. 4 - extreme loading condition - construction with operating basis earthquake (OBE). (a) Operating basis earthquake (OBE). (b) Horizontal earthquake acceleration in upstream direction. (c) No water in reservoir. (d) No headwater or tailwater. (5) Load Condition No. 5 - unusual loading condition - normal operating with



















Stability Considerations a. General requirements . The basic stability requirements for a gravity dam for all conditions of loading are:

(1) That it be safe against overturning at any horizontal plane within the structure, at the base, or at a plane below the base. (2) That it be safe against sliding on any horizontal or near-horizontal plane within the structure at the base or on any rock seam in the foundation. (3) That the allowable unit stresses in the concrete or in the foundation material shall not be exceeded. Characteristic locations within the dam in which a stability criteria check should be considered include planes where there are dam section changes and high concentrated loads. Large galleries and openings within the structure and upstream and downstream slope transitions are specific areas for consideration. b. Stability criteria . The stability criteria for concrete gravity dams for each load condition are listed in Table G.D -1.



















Sliding Stability a. General . The sliding stability is based on a factor of safety ( FS) as a measure of determining the resistance of the structure against sliding. The horizontal components of the loads acting on a dam are resisted by frictional or shearing forces along horizontal or nearly horizontal planes in the body of the dam, on the foundation or on horizontal or nearly horizontal seams in the foundation. It follows that the total magnitude of the forces tending to induce sliding shall be less than the minimum total available resistance along the critical path of sliding. The sliding resistance is a function of the cohesion inherent in the materials and at their contact and the angle of internal friction of the material at the surface of sliding. Definition of sliding factor of safety. (1) The sliding FS is conceptually related to failure, the ratio of the shear strength (tF), and the applied shear stress (t) along the failure planes of a test specimen according to Equation 4-2: F .S . 

 F 



 tan   c  



1  w  u  tan 

 P 

F 



CA 



F c 

where tF = s tan f + c , according to the Mohr-Coulomb Failure Criterion; w = total weight of dam; u = total upthrust force; tan φ = coefficient of internal friction of



















x

h P

W

h/3

B 2

P e R

B 2

Maximum compressive stress = Direct stress + Bending moment Bending moment MB W  6.e  1   A A. B A  B  where W = weight of dam, A = area of dam section, e = eccentricity



W



6.W .e



ELEMENTARY PROFILE OF A GRAVITY DAM





















h

P h 3

P W

J

γh

R B 3

K B 3





















By considering the force triangle, using similar triangles, we have: (W –u )/P = (h/3)/(B/3) 1  1   Bhsg  w   .c. B.h  h 2 2  1 2   B  h   2   or B 2  sg  c   h 2

B 

h

 sg  c  1/2





















 W  u  1  1  0                ( F )  B 

p  

When the reservoir is empty, the only force acting on the elementary profile is its weight, acting through J. In this case, the maximum compressive stress at the heel = W/B(1+1) = 2W/B and the corresponding normal stress at toe is W/B(1-1) =0 The Practical Dam Profile The elementary profile of a gravity dam is a triangle with maximum water surface at its apex. This profile is only theoretical one. For meeting the practoical requirements certain changes have to be made namely: i) for communication, road has to be provided and therefore a top width; ii) for wave action, free board





















Principal and Shear Stress in Dam

Need to redraw





















Therefore

σ 1 = (p v – p.sin 2 α )/cos 2 α σ 1 = p v . sec 2 α – p.tan 2 α -------------------------------------- ----- (H)

Equation (H) is known as the principal stress relationship, which is applicable to both upstream and downstream faces. For the downstream side the worst condition will be when there is no tail water, and hence p will be zero. In this case the major principal stress σ 1 is given by σ 1 = p v . sec 2 α -----------------------------(I) If pe’ is the intensity of hydrodynamic pressure of tail water due to an earthquake, the principal stress at the downstream is given by:























i) Graphical method or ii) Analytical method. We shall consider only the analytical method. For the analytical method, the following steps are carried out:





















( F .S .) 

 M  M

R O

j) The factor factor of safety safety against against sliding is calculated calculated by:





















Reservoir level

Limiting height





















Free Board: is provided on the basis of height of waves and other practical considerations. In practice a free board of between (3 – 5)% of dam height is used





















iv) Therefore ∑V = 244687.5 + 7500 – 90,000 = 162.187.5 kg v) Horizontal water pressure = (γ w x x h2 )/2 = (1000 x 15 2 )/2 = 112,500 g Calculation of moments due to various forces about toe of dam







































































































































































































































































HYDRAULIC STRUCTURE CHAPTER3,4.pdf

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